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The function $\\sigma$ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function $b$ is assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition \\[\n  \\int_1^\\infty\\frac{\\mathrm{d} y}{b(y)}<\\infty \\] implies that "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2305.08458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-05-15T09:00:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3923472901e85bc4b5c437f398c5b33ef7da0edc4bc26ba0afee358a21ad9e97","abstract_canon_sha256":"e5700e03f77b253a6894442188d019fb4fbe8fc376e16e5b0357abca8c36d0d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:10:01.924049Z","signature_b64":"OtMBrVaD8GIhRoMnb+4KqWtBHjwDCUH1yAIja8IULOJesiaOnxcQu6Q/p8Lr9ZS3aO44HEjYmstyT6QMo3kQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42630b030d28c507d4669f1f27e8b816430b895b7fc630c31243db5f8949d4aa","last_reissued_at":"2026-07-05T06:10:01.923613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:10:01.923613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instantaneous everywhere-blowup of parabolic SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Eulalia Nualart, Mohammud Foondun","submitted_at":"2023-05-15T09:00:50Z","abstract_excerpt":"We consider the following stochastic heat equation \\begin{equation*}\n  \\partial_t u(t\\,,x) = \\tfrac12 \\partial^2_x u(t\\,,x) + b(u(t\\,,x)) + \\sigma(u(t\\,,x)) \\dot{W}(t\\,,x), \\end{equation*} defined for $(t\\,,x)\\in(0\\,,\\infty)\\times\\mathbb{R}$, where $\\dot{W}$ denotes space-time white noise. The function $\\sigma$ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function $b$ is assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition \\[\n  \\int_1^\\infty\\frac{\\mathrm{d} y}{b(y)}<\\infty \\] implies that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08458","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.08458/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2305.08458","created_at":"2026-07-05T06:10:01.923667+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.08458v1","created_at":"2026-07-05T06:10:01.923667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08458","created_at":"2026-07-05T06:10:01.923667+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJRQWAYNFDCQ","created_at":"2026-07-05T06:10:01.923667+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJRQWAYNFDCQPVDG","created_at":"2026-07-05T06:10:01.923667+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJRQWAYN","created_at":"2026-07-05T06:10:01.923667+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.00708","citing_title":"Stochastic PDE approach to fluctuating interfaces","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ","json":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ.json","graph_json":"https://pith.science/api/pith-number/IJRQWAYNFDCQPVDGT4PSP2FYCZ/graph.json","events_json":"https://pith.science/api/pith-number/IJRQWAYNFDCQPVDGT4PSP2FYCZ/events.json","paper":"https://pith.science/paper/IJRQWAYN"},"agent_actions":{"view_html":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ","download_json":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ.json","view_paper":"https://pith.science/paper/IJRQWAYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.08458&json=true","fetch_graph":"https://pith.science/api/pith-number/IJRQWAYNFDCQPVDGT4PSP2FYCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/IJRQWAYNFDCQPVDGT4PSP2FYCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ/action/storage_attestation","attest_author":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ/action/author_attestation","sign_citation":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ/action/citation_signature","submit_replication":"https://pith.science/pith/IJRQWAYNFDCQPVDGT4PSP2FYCZ/action/replication_record"}},"created_at":"2026-07-05T06:10:01.923667+00:00","updated_at":"2026-07-05T06:10:01.923667+00:00"}